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# Polygons

## Angles

In a polygon, the line running between non-adjacent points is known as a diagonal. The diagonals drawn from a single vertex to the remaining vertices in an n-sided polygon will divide the figure into n-2 triangles. The sum of the interior angles of a convex polygon is then just (n-2)* 180.

If the side of a polygon is extended past the intersecting adjacent side, it defines the exterior angle of the vertex. Each vertex of a convex polygon has two possible exterior angles, defined by the continuation of each of the sides. These two angles are congruent, however, so the exterior angle of a polygon is defined as one of the two angles. The sum of the exterior angles of any convex polygon is equal to 360°.

Kristin Lewotsky

## KEY TERMS

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Angle

—A geometric figure created by two lines drawn from the same point.

Concave

—A polygon whose at least one angle is larger than the straight angle (180°).

Convex

—A polygon whose all angles are less than the straight angle (180°).

Diagonal

—The line which links-connects any two non-adjacent vertices.

Equiangular

—A polygon is equiangular if all of its angles are identical.

Equilateral

—A polygon is equilateral if all the sides are equal in length.

Parallelogram

—A rectangle with both pair of sides parallel.

Perimeter

—The sum of the length of all sides.

Rectangle

—A parallelogram in which all angles are right angles.

Reflex polygon

—A polygon in which two non-adjacent sides intersect.

Regular polygon

—An equilateral, equiangular polygon.

Rhombus

—A parallelogram whose adjacent sides are equal.

Square

—A four-sided shape whose sides are equal.

Vertex

—The point at which the two sides of an angle meet.